package q583_minDistance;

public class Solution {
    public int minDistance(String word1, String word2) {
        int[][] dp = new int[word1.length() + 1][word2.length() + 1];
        // 注意初始化不要漏了数组最后一个
        for (int i = 0; i <= word1.length(); i++) {
            dp[i][0] = i;
        }

        for (int j = 0; j <= word2.length(); j++) {
            dp[0][j] = j;
        }

        for (int i = 1; i <= word1.length(); i++) {
            for (int j = 1; j <= word2.length(); j++) {
                if (word1.charAt(i - 1) == word2.charAt(j - 1)) {
                    dp[i][j] = dp[i - 1][j - 1];
                }else {
                    // 实际上dp[i - 1][j - 1] + 2一定是最大值
                    // 只需要Math.min(dp[i - 1][j] + 1, dp[i][j - 1] + 1)即可
                    // 不过这里是体现了 要么删掉w1中的一个字符 要么删掉w2中一个字符
                    // 要么双删除 就需要 + 2步
                    dp[i][j] = Math.min(Math.min(dp[i - 1][j] + 1, dp[i][j - 1] + 1), dp[i - 1][j - 1] + 2);
                }

            }
        }

        return dp[word1.length()][word2.length()];
    }
}
